Supersymmetric Higher Spin Models in Three Dimensional Spaces

Ioseph Buchbinder,Timofey Snegirev,Yurii Zinoviev

doi:10.3390/sym10010009

Abstract

We review the component Lagrangian construction of the supersymmetric higher spin models in three-dimensional (3D) Minkowski and anti de Sitter ( A d S ) spaces. The approach is based on the frame-like gauge-invariant formulation, where massive higher spin fields are realized through a system of massless ones. We develop a supersymmetric generalization of this formulation to the Lagrangian construction of the on-shell N = 1 , 3D higher spin supermultiplets. In 3D Minkowski space, we show that the massive supermultiplets can be constructed from one extended massless supermultiplet by adding the mass terms to the Lagrangian and the corresponding corrections to the supertransformations of the fermionic fields. In 3D A d S space, we construct massive supermultiplets using a formulation of the massive fields in terms of the set of gauge-invariant objects (curvatures) in the process of their consistent supersymmetric deformation.

Highlights

As soon as the supersymmetry has been discovered, it aroused an immediate interest in finding the supersymmetric generalization of the known theories
The goal of this review is to present the general methods of supersymmetric Lagrangian construction for massive higher spin fields in 3D Minkowski and anti de Sitter (AdS)
We applied these formulations for the Lagrangian construction of the on-shell N = 1 massless and massive supermultiplets in 3D Minkowski and

Summary

Introduction

As soon as the supersymmetry (see, e.g., the books [1,2,3]) has been discovered, it aroused an immediate interest in finding the supersymmetric generalization of the known theories. Construction of supersymmetric models and the study of their properties on classical and quantum levels became one of the most attractive trends in modern theoretical physics. In the last few decades, there was an essential progress in the higher spin field theory (see, e.g., the reviews [4,5,6]). The purpose of this review is to describe a recent development of Lagrangian construction for massless and massive supersymmetric higher spin models in three-dimensional. In the papers [7,8], the massless N = 1 supersymmetric higher spin field theory was formulated in four-dimensional (4D) Minkowski space. The basic results of these papers were the global on-shell

Objectives

Methods

Conclusion